The Citizens were made to suffer to secure the maximum three points and extended their lead at the summit.
Guardiola’s men have made it a club-record 12 wins in a row which includes eight victories in the Premier League.
Gabriel Jesus put the hosts ahead inside the opening nine minutes and that was enough to beat a stubborn Chris Wilder side, who sit bottom on the Premier League table.
"So difficult [to] win, like we knew it [would be]," the former Bayern Munich and Barcelona coach told Sky Sports after the game. "An incredible victory for us.
"It's amazing after this run of games for us, eight victories in a row, 12 in all competitions, still the players run and fight like animals.
"We conceded one action at the end that was dangerous. So difficult an opponent. We knew it. Every time we play against them we struggle a lot.
"With these [windy] weather conditions, when we woke up we spoke about it today: this will be one of the toughest games we play this season.
"[But] the team was incredibly committed, didn't make mistakes. They were focused on the second balls, the long balls, we won a lot of duels.
"We lacked a little bit to create chances but it's so difficult because they defend with 10 players, defending all the space inside. That is not easy - and after, with the ball, they know exactly what to do."
Manchester City will like to extend their winning streak when they make a trip to Turf Moor to face Burnley on Wednesday.
